When compressing information a distinction is made between lossless and lossy compression techniques. With lossless compression techniques, such as Lempel-Ziv coding or Huffman coding, the original, non-compressed information can be reconstructed from compressed information without errors. Methods of this kind only achieve a high compression rate if the information for compressing comprises specific structures. By contrast high compression rates can be achieved with lossy compression techniques, such as the JPEG method (JPEG-Joint Picture Expert Group), the MPEG2 method (MPEG-Motion Picture Expert Group) or the MC method (MC-Adaptive Audio Coding). However it has to be accepted in this connection that the original, non-compressed information cannot be recovered from the compressed information error free. The errors in the decompressed information often increases as the compression rate increases. Thus with the image compression method JPEG for example, block artifacts can be seen within the decompressed image.
FIG. 1 exemplarily shows a simplified encoding unit of a JPEG encoder JC. In this connection an image IM for compressing is divided into image blocks BB with, for example, 8×8 pixels. Further processing within the JPEG encoder JC is based on these image blocks. Each image block is firstly transformed by the discrete cosine transformation FDCT into the frequency. The coefficients X are produced in the process. Each coefficient X is subjected to a quantization FQ, the quantization, i.e. the quantization factor Q, being controlled by the first table TS1. The quantized coefficient Z is generated hereby. Entropy coding then takes place, for example Huffman coding, by an entropy encoder EC which is controlled with the aid of a second table TS2. Coded image data is written into a file JDS at the outcome of entropy coding.
FIG. 2 shows by way of example a simplified illustration of a decoding unit of a JPEG decoder JD. The encoded image data is read from the file JDS and supplied to the entropy decoder ED for entropy decoding. The entropy decoder ED is controlled by the second table TS2. The quantized coefficients Z are available at the output of the entropy decoder. These are then inversely quantized by an inverse quantization module FIQ, the first table TS1 controlling the inverse quantization. The inverse quantization module FIQ provides reconstructed coefficients Y. These are finally transformed by the inverse discrete cosine transformation IDCT from the frequency domain to the space domain and stored in the reconstructed image IM′ at the appropriate local position.
Quantization is a method that is frequently used within lossy compression techniques. The function of quantization can be illustrated using the following equation:
                    Z        =                  [                      X            Q                    ]                                    (        1        )            where X is the unquantized value or coefficient, Z the quantized value or quantized coefficient and Q the quantization factor. The brackets [ ] in equation (1) denote that all decimal places are deleted, i.e. equation (1) describes a division with an integral calculation result.
If for example the coefficients X are illustrated by 8 bits, the coefficient X can assume a value in the number range from 0 to 255. A value in the number range of the quantized coefficients Z is reduced by quantization as a function of the quantization factor Q. If for example the quantization factor Q=8 and the equation (1) is used to calculate the quantized coefficients, the quantized coefficients Z can only assume a numerical value from 0 to 15. Larger quantization factors Q increase the compression rate.
The following second equation can be used to reconstruct the original unquantized coefficient X:Y=Z*Q  (2),this equation corresponding to an inverse quantization and the reference character Y representing the reconstructed value or reconstructed coefficient.
By deleting the decimal points in equation (1) information is lost, so the reconstructed coefficient Y frequently does not match the coefficient X, i.e. Y•X. A first quantization error QF1 results in this case which, for example, can be numerically determined by the following equation:
                              QF          ⁢                                          ⁢          1                =                                            (                              X                -                Y                            )                        2                    =                                                    (                                  X                  -                                                            Q                      *                                        ⁢                    Z                                                  )                            2                        =                                          (                                  X                  -                                                            Q                      *                                        ⁡                                          [                                              X                        Q                                            ]                                                                      )                            2                                                          (        3        )            
Equation (3) is only one possible type of calculation for the first quantization error QF1. Reference is made by way of example to the literature Shi and Sun, “Image and video compression for multimedia engineering”, CRC-Press, 2000 Chapter 2.2.1.2 for further executions.
To reduce the first quantization error QF1 a correction value can be introduced within the inverse quantization. Two examples are illustrated in more detail in this regard. The quantization error is reduced by the equation
                    Y        =                              (                          Z              +                              1                2                                      )                                                             *                        ⁢            Q                                              (        4        )            
However, equation (4) provides a lower quantization error only for uniformly distributed coefficients X within the quantization interval determined by the quantization factor Q. With non-uniformly distributed coefficients X equation (4) does not supply a minimal quantization error.
A second example is described by the equationY=(Z+KW)*Q  (5)
An adjustment to non-uniformly distributed coefficients X is achieved in this connection by a correction value KW. It is for example known from video encoding software, which is provided with document ITU-T and ISO/IEC JTC1, “JSVM 1 Software”, JVT-N024, January 2005, to definitely set the correction value KW=⅓ for INTRA and INTER-encoded coefficients X and the correction value KW=⅙ for RESIDUAL-encoded coefficients X. The term RESIDUAL encoding should be understood for example as bidirectional encoding.